Problem: Solve for $x$ and $y$ using substitution. ${x+y = -3}$ ${x = -5y-7}$
Solution: Since $x$ has already been solved for, substitute $-5y-7$ for $x$ in the first equation. ${(-5y-7)}{+ y = -3}$ Simplify and solve for $y$ $-5y-7 + y = -3$ $-4y-7 = -3$ $-4y-7{+7} = -3{+7}$ $-4y = 4$ $\dfrac{-4y}{{-4}} = \dfrac{4}{{-4}}$ ${y = -1}$ Now that you know ${y = -1}$ , plug it back into $\thinspace {x = -5y-7}\thinspace$ to find $x$ ${x = -5}{(-1)}{ - 7}$ $x = 5 - 7$ ${x = -2}$ You can also plug ${y = -1}$ into $\thinspace {x+y = -3}\thinspace$ and get the same answer for $x$ : ${x + }{(-1)}{= -3}$ ${x = -2}$